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3 years ago

Solving Quadratic Equations by completing the square xz^2 - 3z - 5 =0

Mathematics

1 answer:

Andrei [34K]3 years ago

8 0

Answer:

x=3z+5

/z^2

Step-by-step explanation:

Let's solve for x.

xz^2−3z−5=0

Step 1: Add 5 to both sides.

xz^2−3z−5+5=0+5

xz^2−3z=5

Step 2: Add 3z to both sides.

xz^2−3z+3z=5+3z

xz^2=3z+5

Step 3: Divide both sides by z^2.

xz^2

/z^2

3z+5/

z^2

3z+5

/z^2

Answer:

x=3z+5

/z^2

(/ means over )

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If y=1/2 when x=2, find y when x=3, given that y varies directly with x

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$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
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3 years ago

A local company makes a candy that is supposed to weigh 1.00 ounces. A random sample of 25 pieces of candy produces a mean of 0.

AysviL [449]

Answer:

$n=(\frac{2.58(0.004)}{0.001})^2 =106.50 \approx 107$

So the answer for this case would be n=107 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\bar X= 0.996$ the sample mean

$s=0.004$ the sample deviation

$n =25$ the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.001 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

We can use as estimator of the real population deviation the sample deviation for this case $\hat \sigma = s$ / The critical value for 99% of confidence interval is given by $z_{\alpha/2}=2.58$ , replacing into formula (b) we got:

$n=(\frac{2.58(0.004)}{0.001})^2 =106.50 \approx 107$

So the answer for this case would be n=107 rounded up to the nearest integer

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3 years ago

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jarptica [38.1K]

Answer:

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b) 20 cm

Step-by-step explanation:

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